Еще раз подытожу.
1) В /resize/resize.php добавляем код в самый конец
$webp_filename = preg_replace('/\.[^.]+$/','',$resized_filename).".webp";
$info = getimagesize($resized_filename);
if (file_exists($webp_filename)) {
} else {
if ($info['mime'] == 'image/jpeg') {
$imagetoconvert = imagecreatefromjpeg($resized_filename);
imagewebp($imagetoconvert, $webp_filename, 80);
imagedestroy($resized_filename);
} elseif ($info['mime'] == 'image/png') {
$imagetoconvert = imagecreatefrompng($resized_filename);
imagewebp($imagetoconvert, $webp_filename, 80);
imagedestroy($resized